Some Consequences of Pump Coherence on Energy Exchange in Nonlinear Optical Processes

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Abstract
The finite coherence time of the driving field plays an important role in the rates of energy exchange taking place in nonlinear processes. As a typical example, the problems of the quantum parametric amplifier and frequency converter driven by a fluctuating pump are considered. A closed hierarchy of equations for the moments of the fields is given, which in turn is used for evaluating the average number of photons per mode and the relative variance as functions of time. Significant deviations from the case where the pump field is coherent are found.

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